A student has a penny, nickel, dime, and quarter distributed two coins apiece to his front two pants pockets. What is the probability that the front right pocket has more than 30¢ in it?
Would it help to rephrase the question?
What is the probability of having a dime and a quarter in the right pocket?
To find the probability that the front right pocket has more than 30¢, we first need to determine the total number of possible coin distributions.
Since each coin is distributed two apiece, there are two cases for the distribution of coins:
1. The penny and nickel are in the front right pocket, and the dime and quarter are in the front left pocket.
2. The penny and dime are in the front right pocket, and the nickel and quarter are in the front left pocket.
Let's calculate the probability for each case:
Case 1: Penny and Nickel in the front right pocket:
There are two possible ways to distribute these two coins in the right pocket: penny-nickel or nickel-penny.
Case 2: Penny and Dime in the front right pocket:
Similarly, there are two possible ways to distribute these two coins in the right pocket: penny-dime or dime-penny.
So, there are a total of 4 possible distributions (2 for each case).
Out of these 4 distributions, we need to determine how many meet the condition of having more than 30¢ in the front right pocket.
For Case 1: Penny and Nickel in the front right pocket:
In both distributions, the total value of coins in the front right pocket will be 6 cents (penny-nickel combination). As this is not more than 30¢, these distributions don't meet the condition.
For Case 2: Penny and Dime in the front right pocket:
In both distributions, the total value of coins in the front right pocket will be 11 cents (penny-dime combination). As this is not more than 30¢, these distributions don't meet the condition either.
Hence, there are 0 distributions out of the 4 that meet the condition.
Therefore, the probability that the front right pocket has more than 30¢ in it is 0.